Thermal convection in a higher-gradient Navier–Stokes fluid

Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term normal spatial derivative term. discussed are Stokes couple stress theory, dipolar Green–Naghdi Fried–Gurtin–Musesti second Fried Gurtin. show that involve same partial differential equations while those similar. However, concentrate boundary conditions which crucial understand five their differences.